The Australian supermodel, 49, announced her engagement to hotel heir Jeffrey in March and has now reportedly wed on the Pacific island in front of family and friends.
A source close to the pair confirmed their nuptials to US Weekly, but gave no further details.
Elle has two sons Flynn, 15, and Aurelius Cy, 10, from her previous relationship with Arpad Busson.
The Britain And Ireland's Next Top Model star originally started dating Jeffrey in 2009, but split in March 2012. After a few months apart, they reunited and went on to get engaged.
The wedding is Elle's second. She was previously married to French fashion photographer Gilles Bensimon.
If the good news is true, we wish Elle and Jeffrey huge congratulations!
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